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Number theory --- 511.6 --- Algebraic number theory --- Algebraic number fields --- Algebraic number theory. --- 511.6 Algebraic number fields

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Number theory --- 511.6 --- #TCPW W1.0 --- #TCPW W1.1 --- #WWIS:ALTO --- Algebraic number fields --- 511.6 Algebraic number fields --- Nombres, Théorie des --- Nombres, Théories des --- Number theory. --- Nombres algébriques, Théorie des

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An especially timely work, the book is an introduction to the theory of p-adic L-functions originated by Kubota and Leopoldt in 1964 as p-adic analogues of the classical L-functions of Dirichlet.Professor Iwasawa reviews the classical results on Dirichlet's L-functions and sketches a proof for some of them. Next he defines generalized Bernoulli numbers and discusses some of their fundamental properties. Continuing, he defines p-adic L-functions, proves their existence and uniqueness, and treats p-adic logarithms and p-adic regulators. He proves a formula of Leopoldt for the values of p-adic L-functions at s=1. The formula was announced in 1964, but a proof has never before been published. Finally, he discusses some applications, especially the strong relationship with cyclotomic fields.

Number theory --- 511.6 --- Algebraic number theory --- L-functions --- Functions, L --- -Number theory --- Algebraic number fields --- Algebraic number theory. --- L-functions. --- 511.6 Algebraic number fields --- -511.6 Algebraic number fields --- Abelian extension. --- Absolute value. --- Algebraic closure. --- Algebraic number field. --- Algebraic number. --- Algebraically closed field. --- Arithmetic function. --- Class field theory. --- Complex number. --- Conjecture. --- Cyclotomic field. --- Dirichlet character. --- Existential quantification. --- Finite group. --- Integer. --- L-function. --- Mellin transform. --- Meromorphic function. --- Multiplicative group. --- P-adic L-function. --- P-adic number. --- Power series. --- Prime number. --- Quadratic field. --- Rational number. --- Real number. --- Root of unity. --- Scientific notation. --- Series (mathematics). --- Special case. --- Subgroup. --- Theorem. --- Topology. --- Nombres, Théorie des